1. Field of Invention
This invention relates to medical diagnostic and monitoring systems. More specifically, this invention is directed to a system and method for reconstructing an aortic blood pressure waveform using a model that is adapted to a specific subject.
2. Description of Related Art
Arterial blood pressure and heart rate are the principal variables used by medical personnel to assess and monitor cardiovascular function and identify adverse cardiovascular events. Such events include tachycardia, bradycardia, arrhythmias, hemorrhage and myocardial ischemia, among others. Ideally, medical personnel would continuously monitor the blood pressure at the root of the aorta, which is the primary driving source for blood flow throughout the body. As illustrated in FIG. 1, blood pressure is produced by the contraction of the heart 1, which ejects a volume of blood into the ascending aorta 2. The aorta 2 distributes the blood to the large arteries of the body, which in turn continually branch into smaller arteries to deliver the blood to the capillaries where oxygen and nutrients are delivered to the tissue. One of these branches is the left subclavian artery 3, which carries blood to the brachial artery 4 in the upper arm. The brachial artery divides into the radial artery 5 and the ulnar artery 6, which then rejoin in the hand from which the five digital arteries 7 emanate to supply the small arteries and capillaries 8 of the fingers.
Except in very special cases when insertion of a catheter into the aorta 2 is warranted for diagnostic purposes, blood pressure measurements are conducted in arteries located some distance from the heart. The most common blood pressure monitoring sites are the brachial artery, radial artery, and finger as illustrated in FIG. 1.
A wide range of patient monitoring devices has been developed for monitoring the blood pressure of patients. Patient monitors usually operate by methods and include devices that measure, analyze and display the electrocardiogram (ECG), intermittent non-invasive blood pressure (NIBP) measurement using a cuff, transcutaneous blood oxygen saturation (SpO2) measurement, continuous direct blood pressure (A-line) measurement, and, in some monitors, non-invasive continuous blood pressure measurement using tonometers.
NIBP monitors take blood pressure measurements periodically and provide numerical values for systolic blood pressure (SBP), mean aortic blood pressure (MBP), and diastolic blood pressure (DBP). When continuous blood pressure measurement is needed, it is continuously monitored with fluid-filled catheters connected to external pressure transducers. The catheter is normally placed in a peripheral vessel such as the radial artery. Continuous blood pressure monitoring can also be performed with tonometers that non-invasively monitor the pressure in a peripheral artery, e.g., the radial artery. (see, Kenmotsu, O., M. Ueda, H. Otsuka, T. Yamamura, D. C. Winter, and J. T. Eckerle, xe2x80x9cArterial Tonometry for Noninvasive, Continuous Blood Pressure Monitoring During Anesthesia,xe2x80x9d Anesthesiology, 1991, Vol. 75, pp 333-340, incorporated herein by reference in its entirety). Other methods have been reported in the literature that are able to provide continuous measurements and recording of the blood pressure in peripheral vessels in the arms and legs. (see, Meyer-Sabellek, W., Schulte, K. L., and Gotzen, R., xe2x80x9cNon-invasive Ambulatory Blood Pressure Monitoring: Technical Possibilities and Problems,xe2x80x9d Journal of Hypertension, 1990, Vol. 8 (Suppl. 6), pp S3-S10, and Nielson, P. E., and Rasmussen, S. M., xe2x80x9cIndirect Measurement of Systolic Blood Pressure by Strain Gage Technique at Finger, Ankle, and Toe in Diabetic Patients without Symptoms of Occlusive Arterial Disease,xe2x80x9d Diabetologia, 1973, Vol. 9, pp 25-29, incorporated herein by reference in their entireties).
However, it is well known that the actual blood pressure in peripheral arteries is different than that at the root of the aorta. (see, MacDonald, D. A., xe2x80x9cBlood Flow in Arteries,xe2x80x9d London, Edward Arnold, 1960, and O""Rourke, Michael F., Raymond P. Kelly, and Alberto P. Avolio, The Arterial Pulse, Philadelphia and London, Lea and Febiger, 1992, both incorporated herein by reference in their entireties).
The MBP decreases slightly as the blood passes from the aorta through the large arteries to the smaller diameter, aortic and radial branches of the arterial tree. As shown in FIG. 1, the pulse pressure increases in amplitude as it passes through the aortic to radial arterial branches after which it begins to decrease in amplitude. (see, Fung, Y. C., Biodynamics: Circulation, Spinger-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984, p.134, incorporated by reference in its entirety). The increase in pulse pressure, or amplification, usually exceeds the small drop in mean blood pressure resulting in an increase in the systolic (maximum) pressure and a smaller magnitude decrease in the diastolic (minimum) pressure. In addition, the shape of the arterial pulse waveform is altered as it passes from the aorta to the periphery. As a result, the pressures measured at peripheral sites may not accurately represent the pressure at the root of the aorta. These amplifications and alterations of the waveform shape have been widely studied and reported by a number of investigators. These changes are caused by the compliant nature of the blood vessels, the terminal impedance of each arterial branch, and wave reflections produced at bifuircations. (see, Taylor, M. G. xe2x80x9cWave Travel in Arteries and the Design of the Cardiovascular System.xe2x80x9d In Pulsatile Blood Flow, ed. Attinger, E. O., McGraw Hill, N.Y., 1964, pp 343-367, incorporated by reference in its entirety).
Modeling studies have taken three approaches to identifying change in an arterial pulse as the pulse propagates.
A first conventional approach has been to develop mathematical descriptions of the physical structure of the vascular system. These models have taken the form of collections of tubes of varying complexity, (see, Taylor, M. G. xe2x80x9cThe Input Impedance of an Assembly of Randomly Branching Elastic Tubes,xe2x80x9d Biophysical Journal, Vol. 6, 1966, pp 29-51 and Avolio, A. P. xe2x80x9cMulti-branched Model of the Human Arterial System,xe2x80x9d Medical and Biological Engineering and Computing, Vol. 18, November 1980, pp 709-718, incorporated by reference in their entireties) and lumped parameter models. (see, Taylor, M. G. xe2x80x9cAn Experimental Determination of the Propagation of Fluid Oscillations in a Tube with a Visco-elastic Wall; Together with an Analysis of the Characteristics Required in an Electrical Analogue,xe2x80x9d Physics in Medicine and Biology, Vol. 4, 1959, pp 62-82, and Ocasio, Wendell C., David R. Rigney, Kevin P. Clark, and Roger G. Mark, xe2x80x9cbpshape_wk4: A Computer Program that Implements a Physiological Model for Analyzing the Shape of Blood Pressure Waveforms,xe2x80x9d Computer Methods and Programs in Biomedicine, Vol. 39 (1993) pp. 169-194, both incorporated by reference in their entireties). Measurements of the cardiovascular system (e.g., vessel dimensions, tissue elasticities, etc.) are then used to develop the coefficients of the model equations. Using the model equations, the approach is able to determine characteristics of the cardiovascular system by modeling the aortic pulse at the aorta root using the characteristics of the aorta pulse at the peripherial artery.
However, this approach is severely limited because of the complexity of the vascular system and the number of parameters that must be known. Most importantly, the cardiovascular system is non-linear and its physical properties vary depending upon the patient""s physiological state at the time of measurement.
A second conventional approach uses lumped parameter elements that represent the major resistive and reactive elements of the vascular system. (see, Strano, Joseph J., Walter Welkowitz, and Sylvan Fich, xe2x80x9cMeasurement and Utilization of In Vivo Blood-Pressure Transfer Functions of Dog and Chicken Aortas,xe2x80x9d IEEE Transactions on Biomedical Engineering, Vol. BME-19, No. 4, July 1972. pp 261-270 incorporated herein in its entirety). This approach allows representation of large portions of the vascular system with relatively few components while providing finer detail in an area of interest. Aortic and peripheral blood pressure data are then used to determine the constants or parameters of the lumped parameters by any number of curve fitting techniques. This approach is useful when information (e.g., the parameters) relating to the major components of the system or a specific segment of the system is of interest.
The third approach essentially models the arterial system as a black box with the aortic blood pressure pulse as the input signal and the peripheral blood pressure pulse as the output signal. Input-output models such as the black box approach have the advantage that no physical knowledge of the arterial system is required. Further, the black box modeling technique requires an assumption that the modeled system is inherently linear. Therefore, the linearity assumption allows the system to be modeled in either direction; that is, the peripheral pulse pressure can be assumed to be the input and the aortic pulse pressure the output or vice versa.
Several mathematical methods have been used to develop an empirical model that describes the workings of the black box. The most common method is the computation of the system""s transfer function in the frequency domain using Fourier transform methods. This technique, widely used in electronics analysis, has been applied to arterial pulse propagation by a number of subjects. (see, for example, Lasance, H. A. J., K. H. Wesseling, C. A. Ascoop, xe2x80x9cPeripheral Pulse Contour Analysis in Determining Stroke Volume,xe2x80x9d Progress Report 5, Inst. Med. Phys., Da Costakade 45, Utrecht, Netherlands, 1976 and U.S. Pat. No. 5,265,011 issued to O""Rourke on Nov. 23, 1993, incorporated by reference in their entireties).
One method for using Fourier methods is described in U.S. Pat. No. 5,265,011. In this patent, the aortic and radial waveforms are obtained from a large number of subjects. The transfer function is then computed from the aorta to the radial artery for each subject using the Fourier transform approach. All of the transforms are then averaged to obtain an average aortic-to-radial transform for the sample population. The universal transform is inverted such that the measured radial waveform is the input and the aortic waveform is the output of the inverse transform. The inverse transform is then transformed back into the time domain to produce a model that provides an estimate of the aortic waveform from the radial waveform.
Input-output models equivalent to the black box technique can be developed in the time-domain using auto-regressive methods (see, Chen, Chen-Huan, et. al., xe2x80x9cEstimation of Central Aortic Pressure Waveform by Mathematical Transformation of Radial Tonometry Pressure: Validation of Generalized Transfer Function,xe2x80x9d Circulation, Vol. 95. No. 7, Apr. 1, 1997, pp. 1827-1836, incorporated herein by reference in its entirety) that use aortic and radial pressure data from a large number of subjects to develop time domain models of the aortic-to-radial waveform propagation. The individual models are transformed into the frequency domain and the resulting transfer functions are averaged as performed in U.S. Pat. No. 5,265,011. The average transfer functions are then inverted and transformed back into the time domain to produce a linear equation that estimates the aortic waveform from the radial waveform.
Use of auto-regressive methods to compute individual aortic to radial model in the time domain is also conventionally known. (see, Hori, Chiori, et.al., xe2x80x9cEstimation of Aortic BP Waveform From Noninvasive Radial Tonometry; Validation of FFT and ARX Methods,xe2x80x9d Proceedings of the IEEE Engineering in Medicine and Biology, 1997, incorporated herein by reference in its entirety). However, Hori et al. perform averaging and inversion in the time domain to produce the average radial-to-aortic model.
Auto-regressive models have been developed for reconstructing aortic waveforms from radial waveforms in baboons. (see, Zhao, Peel, Edgar, and Inada, xe2x80x9cComparison of Direct and Indirect ARX Models for Aortic Blood Pressure Waveform Reconstruction,xe2x80x9d (Abstract) Proceedings of the 1998 Annual Meeting of the Biomedical Engineering Society, Cleveland, Ohio, October, 1998, incorporated herein by reference in its entirety). These models differ from those of earlier investigators in that the radial blood pressure is used as the input to the model and the aortic blood pressure is used as the output. This approach avoids introduction of errors that occur during the inversion of the aortic-to-radial model to produce the radial-to-aortic model. Further, the modeling uses composite radial and aortic signals constructed by concatenating signals from many subjects.
These empirical approaches produce models that are, in essence, averages of the wave propagation characteristics of the subjects comprising the sample population. An example of such an average transfer function from a group of 10 subjects is shown in FIG. 2. When the number of subjects is large and the subjects represent the population as a whole, it is assumed that such models provide reconstructed waveforms of acceptable accuracy in most, if not all, people. This is not, however, the case.
FIG. 3 shows the individual transfer functions for the 10 subjects used to form the average transfer function shown in FIG. 2. As can be readily seen, there is a large variation in both the magnitude and phase relationships between the subjects. As a result, use of an average model produces poor reconstructed aortic blood pressure in subjects who differ from the average of the population. Moreover, the normal variation between subjects is sufficient to produce medically significant errors in estimated blood pressure. (see, Peel, Zhao, Edgar, and Inada, xe2x80x9cFeasibility of Aortic Waveform Reconstruction Using ARX Models,xe2x80x9d (Abstract), Proceedings of the 1998 Annual Meeting of the Biomedical Engineering Society, Cleveland, Ohio, October, 1998; Karamanoglu, Mustafa and Micheal P. Fenely, xe2x80x9cOn-line Synthesis of the Human Ascending Aortic Pulse From the Finger Pulse,xe2x80x9d Hypertension, Vol. 30, No. 6, December 1997, pp 1416-1424; and Stergiopulos, Nikos, Berend E. Westerhof, and Nico Westerhof, xe2x80x9cPhysical Basis of Pressure Transfer From Periphery to Aorta: a Model-based Study,xe2x80x9d Am. J. Physiol. (Hert Circ. Physiol. 43), H1386-1392, 1998, incorporated herein by reference in their entireties). Further, changes in the cardiovascular state within a subject can produce even more significant errors because the approach is affected by the subject""s physiological state. This inherent inaccuracy of average aortic blood pressure reconstruction models severely limits their medical usefulness.
The differences between subjects are a result of the normal physiological differences (e.g., age, vessel properties, etc.) and anatomical differences (e.g., height, weight, sex, etc.) between subjects. Furthermore, the transfer functions for a given subject can change for differing conditions of their cardiovascular system. Within any particular subject, differences are due to changes in the subject""s physiological state (e.g., vasomotor tone, heart rate, peripheral resistance, etc.) that can be produced by disease, introduction of medications, stress, and many other factors.
One approach to producing more accurate estimates of central aortic pressure is to use a mathematical model of the pulse wave propagation path that can be adjusted to a specific subject. One conventional method in accordance with this approach produces a partially individualized model. It uses a linear acoustic model that assumes the pulse propagation path to be a linear combination of viscoelastic tubes terminating in an Windkessel impedance. (see, Karamanoglu, M. and Feneley, M., xe2x80x9cOn-line Synthesis of the Human Ascending Aortic Pressure Pulse from the Finger Pulsexe2x80x9d, Hypertension, 1997, Vol. 30, No. 6, pp 1416-1424, incorporated by reference herein in its entirety). The model first mathematically relates the finger pulse pressure, as measured with a finger cuff blood pressure monitor, to the carotid artery pressure. The aortic pressure is then estimated from the estimated carotid pressure. The parameters of the finger to carotid artery model are estimated using simultaneous measurements of the finger blood pressure and the carotid blood pressure made with a hand-held tonometer. The aortic pressure is estimated from the estimated carotid artery pressure using a population-based, average transfer function of the aortic-to-carotid pulse propagation path.
A second conventional approach for producing an individualized aortic reconstruction model uses a single linear tapered tube model that relates the aortic pressure to the pressure and flow velocity at a point in the peripheral vascular system. (see, Stergiopulos, Nikos, Berend E. Westerhof, and Nico Westerhof, xe2x80x9cPhysical Basis of Pressure Transfer From Periphery to Aorta: a Model-based Study,xe2x80x9d Am. J. Physiol. (Hert Circ. Physiol. 43): H1386-1392, 1998, incorporated by reference herein in its entirety). The model, which estimates the forward and reflected wave transfer functions, is adjusted by estimating the parameters of the tapered tube model from simultaneous measurements of blood pressure and flow velocity at the peripheral site. However, this model is limited to sites that have no major bifurcations (e.g., the radial-ulnar split of the brachial artery) in the propagation path. This limitation is due to the simple, single tube model that is not representative of many peripheral sites. Finally, this model has only been evaluated with simulated aortic and peripheral waveforms produced by a model of the circulatory system.
The empirical universal models and individualized analytical models, while different in the model constructs and pressure measurements used, all assume the cardiovascular system to be linear. Wave propagation in the vascular system is non-linear and the models only work well over limited ranges of cardiovascular states. Moreover, some of the measurements (specifically hand-held tonometry and flow velocity monitoring) are not clinically useful methods for continuous patient monitoring. Finally, and most importantly, the models are limited by their coarse characterization of the vascular system; that is, the conventional approaches that attempt to personalize the model to the subject also attempt to characterize the propagation path solely from the two pressures measured at the aorta and the peripheral measurement site.
A common feature of conventional methods that model wave propagation in the peripheral arteries with linear models is the assumption of linearity, i.e., that the cardiovascular system may be accurately modeled as a linear system, and the assumption of stationarity, i.e., the invariance of the arterial system over time and subjects. The assumption of linearity is generally valid if the range of pressure variations is small. The assumption of stationarity is valid provided that assumptions about the state of a cardiovascular system do not change over patients or over time. However, it is conventionally understood these assumptions do not hold for physiological systems.
The most notable source of non-linearity in the cardiovascular system is the dependence of the vessel wall elasticity and compliance on the instantaneous blood pressure and vasomotor tone. (see Callaghan, F. J., L. A. Geddes, C. F. Babbs, and J. D. Bourland, xe2x80x9cRelationship Between Pulse-wave Velocity and Arterial Elasticity,xe2x80x9d Med. and Biol. Eng. and Comput., 1986, Vol. 24, pp 248-254, incorporated by reference in its entirety). Vessel wall elasticity is also a function of age and possibly gender. Damping, while usually ascribed to viscous losses in the vessel wall and fluid viscosity, is also influenced by the adhesion, or tethering of the vessel to the surrounding tissue. The surrounding tissue also contributes elastic and inertial components to the wall elasticity; these factors are heavily dependent upon body morphology and muscle tone. The resistive component of tube models is assumed to be a constant. However, the pressure drop in fluid systems is a function of the square of the flow velocity and produces a varying resistance over the period of a blood pressure pulse because the blood flow varies widely over the cardiac cycle.
Further, the structure of the arterial tree is a source of non-linearity. The arterial tree is a continuously branching system of tubes rather than the simple series of tubes assumed by most conventional models. Each major arterial branch includes sub-branches at which the primary artery splits into two or perhaps three sub-branches. As a general rule, the daughter tubes, i.e., the sub-branches produced by branching, at major bifurcations, are smaller in diameter than the parent tube. However, the daughter tubes also have a combined cross-sectional area that is larger than the parent tube.
The principal effect at major branching is the large difference in the forward and reverse impedances. Therefore, reflections are produced at major branch bifurcations. Between these major branch bifurcations, there are many smaller side branch tubes that have cross-sectional areas that are much smaller than the parent tube. The geometry of a subject""s arterial tree can be changed by changes in body position, which introduce significant bends into the tubes and, which may partially or completely occlude one or more branches. Moreover, the geometry of the branching is highly variable between subjects.
The assumption of stationarity is the greatest shortcoming of conventional models for aortic blood pressure reconstruction. This is because the cardiovascular system is highly dynamic and has numerous control mechanisms for adapting to the changing metabolic needs of the subject. These control mechanisms alter not only the heart rate and stroke volume, but also the mechanical characteristics of the large and small vessels. The vascular changes influence the pulse wave propagation velocity, vessel resistance and the terminal impedance of the pulse wave propagation path. Vascular control mechanisms also respond to medications, disease processes, and blood loss. As a result, aortic blood pressure reconstruction requires a model that is adaptable to a subject and adjustable to changes in a subject""s state. This requires monitoring of the subject""s cardiovascular state and a device for adapting the reconstruction model to the changes in cardiovascular state. The invention is directed at providing such an adaptable and adjustable aortic blood pressure reconstruction model.
Conventional models that predict aortic pressure from peripheral pressures have been only partially successful, in part, because of sources of variability, both between subjects and within a subject over time. These shortcomings of the conventional aortic blood pressure reconstruction are overcome by the present invention.
In an exemplary embodiment of the invention, other physiological measurements are performed in conjunction with continuous A-line or tonometer blood pressure monitoring. For example, the exemplary embodiments use the ECG, NIBP, and oximetry. Specifically, the ECG provides a time reference for the start of each blood pressure pulse as it leaves the root of the aorta. The occlusion cuff of a NIBP monitor serves as a plethysmograph, which can produce brachial blood pressure waveforms when the pressure is held constant at a low pressure. Pulse oximeters, as part of their measurement apparatus, produce a continuous plethysmographic measurement of the blood pressure waveform in the finger. The shortcomings of conventional linear models are overcome using the measurements provided by the ECG, the occlusion cuff of the NIBP monitor and the pulse oximeters.
Accordingly, the invention relates to methods and systems for reconstructing and verifying aortic blood pressure waveforms from peripheral blood pressure waveform data using mathematical models. These mathematical models combine analytical models of pulse wave propagation in the cardiovascular system with empirical models derived from measurements taken from a population of human subjects and from the individual subject being modeled. When used to reconstruct the aortic pressure of a given subject, the mathematical models are adjusted to the subject and the subject""s physiological state based upon measurements performed on the subject""s cardiovascular system.
An empirical aortic waveform reconstruction model is obtained from measurements performed on a large population of subjects. The empirical models are personalized to subjects by normalizing the model using the subjects"" wave-propagation characteristics and other information. Subsequently, the normalized empirical models are combined into a single population average normalized model. The normalization is performed with the aid of mathematical descriptions of the vascular system and measurements that account for individual variations, non-uniformities, and non-linearities of the cardiovascular system. When used for reconstruction of a specific subject""s aortic blood pressure, the general, normalized model is adjusted using measurements performed on the specific subject. The reconstructed aortic waveform is verified by using it to reproduce the waveform at one point in the vascular system and comparing that waveform to a waveform measured at that point.